crypto/dh/dh_gen.c

   1 /*
   2  * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the Apache License 2.0 (the "License").  You may not use
   5  * this file except in compliance with the License.  You can obtain a copy
   6  * in the file LICENSE in the source distribution or at
   7  * https://www.openssl.org/source/license.html
   8  */
   9
  10 /*
  11  * NB: These functions have been upgraded - the previous prototypes are in
  12  * dh_depr.c as wrappers to these ones.  - Geoff
  13  */
  14
  15 #include <stdio.h>
  16 #include "internal/cryptlib.h"
  17 #include <openssl/bn.h>
  18 #include "dh_locl.h"
  19
  20 static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
  21                                 BN_GENCB *cb);
  22
  23 int DH_generate_parameters_ex(DH *ret, int prime_len, int generator,
  24                               BN_GENCB *cb)
  25 {
  26     if (ret->meth->generate_params)
  27         return ret->meth->generate_params(ret, prime_len, generator, cb);
  28     return dh_builtin_genparams(ret, prime_len, generator, cb);
  29 }
  30
  31 /*-
  32  * We generate DH parameters as follows
  33  * find a prime p which is prime_len bits long,
  34  * where q=(p-1)/2 is also prime.
  35  * In the following we assume that g is not 0, 1 or p-1, since it
  36  * would generate only trivial subgroups.
  37  * For this case, g is a generator of the order-q subgroup if
  38  * g^q mod p == 1.
  39  * Or in terms of the Legendre symbol: (g/p) == 1.
  40  *
  41  * Having said all that,
  42  * there is another special case method for the generators 2, 3 and 5.
  43  * Using the quadratic reciprocity law it is possible to solve
  44  * (g/p) == 1 for the special values 2, 3, 5:
  45  * (2/p) == 1 if p mod 8 == 1 or 7.
  46  * (3/p) == 1 if p mod 12 == 1 or 11.
  47  * (5/p) == 1 if p mod 5 == 1 or 4.
  48  * See for instance: https://en.wikipedia.org/wiki/Legendre_symbol
  49  *
  50  * Since all safe primes > 7 must satisfy p mod 12 == 11
  51  * and all safe primes > 11 must satisfy p mod 5 != 1
  52  * we can further improve the condition for g = 2, 3 and 5:
  53  * for 2, p mod 24 == 23
  54  * for 3, p mod 12 == 11
  55  * for 5, p mod 60 == 59
  56  */
  57 static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
  58                                 BN_GENCB *cb)
  59 {
  60     BIGNUM *t1, *t2;
  61     int g, ok = -1;
  62     BN_CTX *ctx = NULL;
  63
  64     ctx = BN_CTX_new();
  65     if (ctx == NULL)
  66         goto err;
  67     BN_CTX_start(ctx);
  68     t1 = BN_CTX_get(ctx);
  69     t2 = BN_CTX_get(ctx);
  70     if (t2 == NULL)
  71         goto err;
  72
  73     /* Make sure 'ret' has the necessary elements */
  74     if (!ret->p && ((ret->p = BN_new()) == NULL))
  75         goto err;
  76     if (!ret->g && ((ret->g = BN_new()) == NULL))
  77         goto err;
  78
  79     if (generator <= 1) {
  80         DHerr(DH_F_DH_BUILTIN_GENPARAMS, DH_R_BAD_GENERATOR);
  81         goto err;
  82     }
  83     if (generator == DH_GENERATOR_2) {
  84         if (!BN_set_word(t1, 24))
  85             goto err;
  86         if (!BN_set_word(t2, 23))
  87             goto err;
  88         g = 2;
  89     } else if (generator == DH_GENERATOR_5) {
  90         if (!BN_set_word(t1, 60))
  91             goto err;
  92         if (!BN_set_word(t2, 59))
  93             goto err;
  94         g = 5;
  95     } else {
  96         /*
  97          * in the general case, don't worry if 'generator' is a generator or
  98          * not: since we are using safe primes, it will generate either an
  99          * order-q or an order-2q group, which both is OK
 100          */
 101         if (!BN_set_word(t1, 12))
 102             goto err;
 103         if (!BN_set_word(t2, 11))
 104             goto err;
 105         g = generator;
 106     }
 107
 108     if (!BN_generate_prime_ex(ret->p, prime_len, 1, t1, t2, cb))
 109         goto err;
 110     if (!BN_GENCB_call(cb, 3, 0))
 111         goto err;
 112     if (!BN_set_word(ret->g, g))
 113         goto err;
 114     ok = 1;
 115  err:
 116     if (ok == -1) {
 117         DHerr(DH_F_DH_BUILTIN_GENPARAMS, ERR_R_BN_LIB);
 118         ok = 0;
 119     }
 120
 121     BN_CTX_end(ctx);
 122     BN_CTX_free(ctx);
 123     return ok;
 124 }